论文标题
关于雷利（Rayleigh）的抑制作用 - 泰勒（Taylor）不稳定性通过水平磁场中的不抗性MHD流体：粘性情况
On Inhibition of Rayleigh--Taylor Instability by a Horizontal Magnetic Field in Non-resistive MHD Fluids: the Viscous Case
论文作者
论文摘要
是否可以通过水平磁场抑制雷利 - 泰勒（RT）不稳定的现象可以在数学上进行数学验证\ cite {Wyc}。在本文中，我们通过\ emph {navier（slip）边界条件}证明了（非线性）不均匀，不可压缩的，\ emph {viscous case}的抑制现象。 More precisely, we show that there is a critical number of field strength $m_{\mm{C}}$, such that if the strength $|m|$ of a horizontal magnetic field is bigger than $m_{\mm{C}}$, then the small perturbation solution around the magnetic RT equilibrium state is {algebraically} stable in time.此外，我们还为情况提供了非线性不稳定性结果，$ | m | \ in [0，m _ {\ mm {c}}}）$。不稳定性结果表明，如果强度太小，水平磁场将无法抑制RT的不稳定性。
It is still open whether the phenomenon of inhibition of Rayleigh--Taylor (RT) instability by a horizontal magnetic field can be mathematically verified for a non-resistive \emph{viscous} magnetohydrodynamic (MHD) fluid in a two-dimensional (2D) horizontal slab domain, since it was roughly proved in the linearized case by Wang in \cite{WYC}. In this paper, we prove such inhibition phenomenon by the (nonlinear) inhomogeneous, incompressible, \emph{viscous case} with \emph{Navier (slip) boundary condition}. More precisely, we show that there is a critical number of field strength $m_{\mm{C}}$, such that if the strength $|m|$ of a horizontal magnetic field is bigger than $m_{\mm{C}}$, then the small perturbation solution around the magnetic RT equilibrium state is {algebraically} stable in time. In addition, we also provide a nonlinear instability result for the case $|m|\in[0, m_{\mm{C}})$. The instability result presents that a horizontal magnetic field can not inhibit the RT instability, if it's strength is too small.
